Report of the fit

Fit summary

Description: PV19 version x, parameters for NNLL. Trying the parameters that gave chi2 = 1.65708 for replica 0 when minimised with ceres. Minuit with the same parameters, starting from the same fitcofig, didn’t converge.
Minimiser: ceres
Random seed: 1234
Maximum values allowed for q_T / Q: 0.2
Cut on the error function: 2.8
Parameterisation: PV19x
Initial parameters fluctuations: True
Explicit formula:

f_{\rm NP}(x,\zeta, b_T)= \Biggl( \frac{1-\lambda}{1 + g_1(x) b_T^2/4} + \lambda \exp \left(-g_{1B}(x) b_T^2 / 4 \right)\Biggr) \exp\left[- g_2 \log\left(\frac{\zeta}{Q_0^2}\right) b_T^2/4 - g_{2B} \log\left(\frac{\zeta}{Q_0^2}\right) b_T^4/4 \right]g_1(x) = \frac{N_1}{x\sigma} \exp\left[ - \frac{\ln^2\left(\frac{x}{\alpha}\right)}{2 \sigma^2} \right]g_{1B}(x) = \frac{N_{1B}}{x\sigma_B} \exp\left[ - \frac{\ln^2\left(\frac{x}{\alpha_B}\right)}{2 \sigma_B^2} \right]Q_0^2 = 1\;{\rm GeV}^2 t_0 prescription: True

g_2 N_1 \alpha \sigma \lambda N_{1B} \alpha_B \sigma_B g_{2B}
0.005144 0.68535248 0.21943481 0.3329461 0.66627605 0.0387879 0.075758463 0.34845635 0.019224141

Theory summary

Collinear PDF set: MMHT2014nlo68cl member 0
Collinear FF set: DSS14_NLO_PiSum member 0
b^* prescription: bstarmin
Perturbative order: NNLL
Reference value of the fine-structure constant: \alpha(Q = 91.1876\;{\rm GeV}) = 0.00776578395589 (running True)

Global statistical estimators

N_{rep} = 200
\chi_{0}^2 = 1.6571
\chi_{mean}^2 = 1.6392
\langle\chi^2\rangle \pm \sigma_{\chi^2} = 1.6893 \pm 0.0455
\langle E \rangle \pm \sigma_{E} = 2.5699 \pm 0.1394

Parameters

Parameter Central replica Average over replicas Fixed
g_2 -0.09141059 -0.07516749 \pm 0.02324989 False
N_1 5.3603904 13.82973829 \pm 54.00740774 False
\alpha 1.0686624 2.09075861 \pm 5.98685056 False
\sigma 0.93749188 0.86044179 \pm 0.26526407 False
\lambda 0.49349918 0.50479593 \pm 0.07450152 False
N_{1B} 0.040693304 0.03976956 \pm 0.22640261 False
\alpha_B 0.052748277 0.25774191 \pm 1.26648474 False
\sigma_B 0.56928194 1.94596686 \pm 24.52534851 False
g_{2B} 0.034354286 0.03215853 \pm 0.01056618 False
Fitted parameter correlation matrix

Fit properties

Global \chi^2 distribution
Global error function distribution
g_2 distribution
N_1 distribution
\alpha distribution
\sigma distribution
\lambda distribution
N_{1B} distribution
\alpha_B distribution
\sigma_B distribution
g_{2B} distribution

Table of \chi^2’s

Central-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.4814 0.0307 0.5121
E605_Q_8_9 8 0.9948 0.0176 1.0124
E605_Q_10.5_11.5 10 0.494 0.1396 0.6336
E288_200_Q_4_5 4 0.9291 0.8595 1.7885
E288_200_Q_5_6 5 2.3107 0.3547 2.6654
E288_200_Q_6_7 6 0.7947 0.2112 1.0059
E288_200_Q_7_8 7 0.9887 0.032 1.0206
E288_200_Q_8_9 8 0.7359 0.0059 0.7419
E288_300_Q_4_5 4 0.7784 0.3426 1.121
E288_300_Q_5_6 5 1.3997 0.1 1.4997
E288_300_Q_6_7 6 1.042 0.0398 1.0818
E288_300_Q_7_8 7 0.3439 0.0425 0.3864
E288_300_Q_8_9 8 0.3919 0.0384 0.4303
E288_400_Q_5_6 5 0.9446 0.001 0.9456
E288_400_Q_6_7 6 0.5281 0.0068 0.5349
E288_400_Q_7_8 7 0.2499 0.0139 0.2637
E288_400_Q_8_9 8 0.5613 0.0126 0.574
E288_400_Q_11_12 11 0.5749 0.0068 0.5817
E288_400_Q_12_13 12 0.5394 0.0113 0.5507
E288_400_Q_13_14 12 0.3455 0.0363 0.3817
STAR_510 7 1.192 0.0136 1.2056
CDF_RunI 25 0.6522 0.1484 0.8006
CDF_RunII 26 1.2759 0.0074 1.2833
D0_RunI 12 0.6652 0.0018 0.667
D0_RunII 5 0.9114 0.2907 1.2022
D0_RunIImu 3 0.1197 0.0844 0.2041
LHCb_7TeV 7 1.945 0.8427 2.7877
LHCb_8TeV 7 1.9245 1.453 3.3775
LHCb_13TeV 7 1.4927 0.2893 1.782
CMS_7TeV 4 2.8928 0 2.8928
CMS_8TeV 4 1.4845 0.1782 1.6627
ATLAS_7TeV_y_0_1 6 6.9545 1.0911 8.0455
ATLAS_7TeV_y_1_2 6 4.9261 0.4825 5.4086
ATLAS_7TeV_y_2_2.4 6 1.8076 0.0099 1.8176
ATLAS_8TeV_y_0_0.4 6 4.7783 0.9776 5.756
ATLAS_8TeV_y_0.4_0.8 6 6.6974 1.5469 8.2443
ATLAS_8TeV_y_0.8_1.2 6 4.3581 0.6689 5.027
ATLAS_8TeV_y_1.2_1.6 6 2.9433 0.4249 3.3682
ATLAS_8TeV_y_1.6_2 6 2.5563 0.2696 2.8259
ATLAS_8TeV_y_2_2.4 6 1.2834 0.1619 1.4453
ATLAS_8TeV_Q_46_66 4 0.7685 0.0368 0.8053
ATLAS_8TeV_Q_116_150 8 1.1501 0.0073 1.1574
Total 319 - - 1.6571
Mean-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.632 0.0898 0.7218
E605_Q_8_9 8 1.2311 0.048 1.2791
E605_Q_10.5_11.5 10 0.3645 0.1015 0.466
E288_200_Q_4_5 4 0.4534 0.4421 0.8956
E288_200_Q_5_6 5 1.3314 0.2707 1.6021
E288_200_Q_6_7 6 0.5796 0.1765 0.7562
E288_200_Q_7_8 7 0.9051 0.0334 0.9385
E288_200_Q_8_9 8 0.9342 0.0128 0.9469
E288_300_Q_4_5 4 0.5336 0.16 0.6935
E288_300_Q_5_6 5 1.1461 0.0595 1.2056
E288_300_Q_6_7 6 0.9439 0.0265 0.9704
E288_300_Q_7_8 7 0.326 0.033 0.359
E288_300_Q_8_9 8 0.2817 0.0393 0.321
E288_400_Q_5_6 5 1.0811 0.0171 1.0982
E288_400_Q_6_7 6 0.6129 0.0299 0.6427
E288_400_Q_7_8 7 0.2957 0.0462 0.3419
E288_400_Q_8_9 8 0.7447 0.0408 0.7856
E288_400_Q_11_12 11 0.839 0.0141 0.8531
E288_400_Q_12_13 12 0.8667 0.0173 0.884
E288_400_Q_13_14 12 0.8895 0.066 0.9555
STAR_510 7 1.1469 0.0372 1.1841
CDF_RunI 25 0.5739 0.1421 0.716
CDF_RunII 26 1.2356 0.006 1.2416
D0_RunI 12 0.6384 0.0007 0.6391
D0_RunII 5 1.0845 0.2943 1.3788
D0_RunIImu 3 0.022 0.0333 0.0554
LHCb_7TeV 7 1.682 0.8471 2.5291
LHCb_8TeV 7 1.8199 1.3821 3.202
LHCb_13TeV 7 1.3368 0.2691 1.6059
CMS_7TeV 4 2.8768 0 2.8768
CMS_8TeV 4 1.5098 0.1835 1.6933
ATLAS_7TeV_y_0_1 6 6.9378 1.0929 8.0307
ATLAS_7TeV_y_1_2 6 4.8183 0.4907 5.3091
ATLAS_7TeV_y_2_2.4 6 1.6825 0.01 1.6924
ATLAS_8TeV_y_0_0.4 6 4.7797 1.0131 5.7928
ATLAS_8TeV_y_0.4_0.8 6 6.5292 1.5932 8.1224
ATLAS_8TeV_y_0.8_1.2 6 4.3571 0.6881 5.0452
ATLAS_8TeV_y_1.2_1.6 6 2.9724 0.4409 3.4133
ATLAS_8TeV_y_1.6_2 6 2.4292 0.2746 2.7039
ATLAS_8TeV_y_2_2.4 6 1.1482 0.1534 1.3016
ATLAS_8TeV_Q_46_66 4 0.716 0.0522 0.7682
ATLAS_8TeV_Q_116_150 8 1.1316 0.0063 1.1379
Total 319 - - 1.6392
Average-over-replicas \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.4556 \pm 0.2212 0.159 \pm 0.2208 0.6146 \pm 0.1527
E605_Q_8_9 8 1.0508 \pm 0.2761 0.1109 \pm 0.1499 1.1617 \pm 0.2573
E605_Q_10.5_11.5 10 0.4775 \pm 0.2324 0.1831 \pm 0.2711 0.6606 \pm 0.2267
E288_200_Q_4_5 4 0.5964 \pm 1.195 1.0654 \pm 1.1838 1.6617 \pm 0.4361
E288_200_Q_5_6 5 2.123 \pm 0.6806 0.4521 \pm 0.6138 2.5751 \pm 0.3591
E288_200_Q_6_7 6 0.6674 \pm 0.384 0.283 \pm 0.3339 0.9504 \pm 0.2252
E288_200_Q_7_8 7 0.8673 \pm 0.2562 0.1206 \pm 0.1695 0.9879 \pm 0.2174
E288_200_Q_8_9 8 0.6849 \pm 0.1217 0.0712 \pm 0.0809 0.7561 \pm 0.1038
E288_300_Q_4_5 4 0.5264 \pm 0.7277 0.5038 \pm 0.6447 1.0302 \pm 0.2686
E288_300_Q_5_6 5 1.1632 \pm 0.4169 0.2684 \pm 0.3878 1.4317 \pm 0.3136
E288_300_Q_6_7 6 0.8485 \pm 0.3641 0.1685 \pm 0.2666 1.017 \pm 0.2918
E288_300_Q_7_8 7 0.2259 \pm 0.2243 0.142 \pm 0.231 0.3679 \pm 0.1665
E288_300_Q_8_9 8 0.3352 \pm 0.1639 0.1136 \pm 0.1777 0.4488 \pm 0.0864
E288_400_Q_5_6 5 0.7287 \pm 0.4086 0.1561 \pm 0.2214 0.8847 \pm 0.3408
E288_400_Q_6_7 6 0.4005 \pm 0.3474 0.11 \pm 0.1457 0.5106 \pm 0.3249
E288_400_Q_7_8 7 0.1753 \pm 0.2838 0.1047 \pm 0.1499 0.2799 \pm 0.244
E288_400_Q_8_9 8 0.5189 \pm 0.1827 0.0846 \pm 0.1097 0.6035 \pm 0.1553
E288_400_Q_11_12 11 0.5344 \pm 0.1127 0.0435 \pm 0.0574 0.5779 \pm 0.1089
E288_400_Q_12_13 12 0.5238 \pm 0.0829 0.0482 \pm 0.0655 0.572 \pm 0.0699
E288_400_Q_13_14 12 0.3349 \pm 0.1037 0.0767 \pm 0.0835 0.4116 \pm 0.1145
STAR_510 7 1.0669 \pm 0.2009 0.1136 \pm 0.1867 1.1806 \pm 0.0986
CDF_RunI 25 0.63 \pm 0.174 0.1903 \pm 0.171 0.8203 \pm 0.0467
CDF_RunII 26 1.2715 \pm 0.2155 0.0572 \pm 0.0721 1.3287 \pm 0.2078
D0_RunI 12 0.6294 \pm 0.1128 0.0654 \pm 0.0867 0.6947 \pm 0.0725
D0_RunII 5 0.6399 \pm 0.6421 0.4921 \pm 0.5654 1.132 \pm 0.28
D0_RunIImu 3 -0.3292 \pm 0.5872 0.5219 \pm 0.5419 0.1926 \pm 0.2952
LHCb_7TeV 7 1.8249 \pm 0.7541 1.0155 \pm 0.7196 2.8404 \pm 0.2052
LHCb_8TeV 7 1.9658 \pm 0.9316 1.526 \pm 0.8742 3.4918 \pm 0.3644
LHCb_13TeV 7 1.4009 \pm 0.447 0.3664 \pm 0.4275 1.7673 \pm 0.0982
CMS_7TeV 4 2.9017 \pm 0.0488 0.0 \pm 0.0 2.9017 \pm 0.0488
CMS_8TeV 4 1.4179 \pm 0.2711 0.2564 \pm 0.2307 1.6742 \pm 0.1121
ATLAS_7TeV_y_0_1 6 6.9701 \pm 0.8299 1.1829 \pm 0.5859 8.153 \pm 0.5601
ATLAS_7TeV_y_1_2 6 4.9796 \pm 0.4804 0.5661 \pm 0.3526 5.5457 \pm 0.3456
ATLAS_7TeV_y_2_2.4 6 1.8507 \pm 0.1667 0.0299 \pm 0.0383 1.8806 \pm 0.1637
ATLAS_8TeV_y_0_0.4 6 4.9952 \pm 0.6953 1.0249 \pm 0.4628 6.0201 \pm 0.4915
ATLAS_8TeV_y_0.4_0.8 6 6.7879 \pm 0.7674 1.6129 \pm 0.6929 8.4007 \pm 0.3869
ATLAS_8TeV_y_0.8_1.2 6 4.3167 \pm 0.4064 0.6347 \pm 0.3148 4.9514 \pm 0.2649
ATLAS_8TeV_y_1.2_1.6 6 2.9257 \pm 0.3964 0.4608 \pm 0.3231 3.3865 \pm 0.2378
ATLAS_8TeV_y_1.6_2 6 2.6784 \pm 0.4567 0.3277 \pm 0.3152 3.0061 \pm 0.3298
ATLAS_8TeV_y_2_2.4 6 1.5619 \pm 0.6057 0.2441 \pm 0.217 1.806 \pm 0.5764
ATLAS_8TeV_Q_46_66 4 0.6044 \pm 0.3186 0.2233 \pm 0.319 0.8277 \pm 0.0999
ATLAS_8TeV_Q_116_150 8 1.0685 \pm 0.1686 0.1089 \pm 0.1584 1.1774 \pm 0.0561
Total 319 - - 1.6893 \pm 0.0455

TMDs in k_T space

TMD PDF of the d at Q = 2 GeV and x = 0.001
TMD PDF of the d at Q = 2 GeV and x = 0.01
TMD PDF of the d at Q = 2 GeV and x = 0.1
TMD PDF of the d at Q = 2 GeV and x = 0.5
TMD PDF of the d at Q = 2 GeV and x = 0.9

Data-theory comparison

E605_Q_7_8 data-theory comparison
E605_Q_8_9 data-theory comparison
E605_Q_10.5_11.5 data-theory comparison
E288_200_Q_4_5 data-theory comparison
E288_200_Q_5_6 data-theory comparison
E288_200_Q_6_7 data-theory comparison
E288_200_Q_7_8 data-theory comparison
E288_200_Q_8_9 data-theory comparison
E288_300_Q_4_5 data-theory comparison
E288_300_Q_5_6 data-theory comparison
E288_300_Q_6_7 data-theory comparison
E288_300_Q_7_8 data-theory comparison
E288_300_Q_8_9 data-theory comparison
E288_400_Q_5_6 data-theory comparison
E288_400_Q_6_7 data-theory comparison
E288_400_Q_7_8 data-theory comparison
E288_400_Q_8_9 data-theory comparison
E288_400_Q_11_12 data-theory comparison
E288_400_Q_12_13 data-theory comparison
E288_400_Q_13_14 data-theory comparison
STAR_510 data-theory comparison
CDF_RunI data-theory comparison
CDF_RunII data-theory comparison
D0_RunI data-theory comparison
D0_RunII data-theory comparison
D0_RunIImu data-theory comparison
LHCb_7TeV data-theory comparison
LHCb_8TeV data-theory comparison
LHCb_13TeV data-theory comparison
CMS_7TeV data-theory comparison
CMS_8TeV data-theory comparison
ATLAS_7TeV_y_0_1 data-theory comparison
ATLAS_7TeV_y_1_2 data-theory comparison
ATLAS_7TeV_y_2_2.4 data-theory comparison
ATLAS_8TeV_y_0_0.4 data-theory comparison
ATLAS_8TeV_y_0.4_0.8 data-theory comparison
ATLAS_8TeV_y_0.8_1.2 data-theory comparison
ATLAS_8TeV_y_1.2_1.6 data-theory comparison
ATLAS_8TeV_y_1.6_2 data-theory comparison
ATLAS_8TeV_y_2_2.4 data-theory comparison
ATLAS_8TeV_Q_46_66 data-theory comparison
ATLAS_8TeV_Q_116_150 data-theory comparison